Solve for $x$ and $y$ using elimination. ${-5x-4y = -37}$ ${2x+y = 10}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-5x-4y = -37}$ $8x+4y = 40$ Add the top and bottom equations together. $3x = 3$ $\dfrac{3x}{{3}} = \dfrac{3}{{3}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-5x-4y = -37}\thinspace$ to find $y$ ${-5}{(1)}{ - 4y = -37}$ $-5-4y = -37$ $-5{+5} - 4y = -37{+5}$ $-4y = -32$ $\dfrac{-4y}{{-4}} = \dfrac{-32}{{-4}}$ ${y = 8}$ You can also plug ${x = 1}$ into $\thinspace {2x+y = 10}\thinspace$ and get the same answer for $y$ : ${2}{(1)}{ + y = 10}$ ${y = 8}$